TY  - BOOK
AU  - Cutland,Nigel J.
ED  - SpringerLink (Online service)
TI  - Loeb Measures in Practice: Recent Advances
T2  - Lecture Notes in Mathematics,
SN  - 9783540445319
AV  - QA8.9-10.3 
U1  - 511.3 23
PY  - 2000///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Finance
KW  - Logic, Symbolic and mathematical
KW  - Distribution (Probability theory)
KW  - Mathematical Logic and Foundations
KW  - Real Functions
KW  - Probability Theory and Stochastic Processes
KW  - Quantitative Finance
N1  - Loeb Measures: Introduction -- Nonstandard Analysis -- Construction of Loeb Measures -- Loeb Integration Theory -- Elementary Applications. Stochastic Fluid Mechanics: Introduction -- Solution of the Deterministic Navier-Stokes Equations -- Solution of the Stochastic Navier-Stokes Equations -- Stochastic Euler Equations -- Statistical Solutions -- Attractors for the Navier-Stokes Equations -- Measure Attractors for Stochastic Navier-Stokes Equations -- Stochastic Attractors for Navier-Stokes Equations -- Attractors for the 3-dimensional Stochastic Navier-Stokes Equations. Stochastic Calculus of Variations: Introduction -- Flat Integral Representation of Wiener Measure -- The Wiener Sphere -- Brownian Motion on the Wiener Sphere and the Infinite Dimensional Ornstein-Uhlenbeck Process -- Malliavin Calculus. Mathematical Finance Theory: Introduction -- The Cox-Ross-Rubinstein Models -- Options and Contingent Claims -- The Black-Scholes Model... The complete table of contents can be found on the Internet: http://www.springer.de
N2  - This expanded version of the 1997 European Mathematical Society Lectures given by the author in Helsinki, begins with a self-contained introduction to nonstandard analysis (NSA) and the construction of Loeb Measures, which are rich measures discovered in 1975 by Peter Loeb, using techniques from NSA. Subsequent chapters sketch a range of recent applications of Loeb measures due to the author and his collaborators, in such diverse fields as (stochastic) fluid mechanics, stochastic calculus of variations ("Malliavin" calculus) and the mathematical finance theory. The exposition is designed for a general audience, and no previous knowledge of either NSA or the various fields of applications is assumed
UR  - http://dx.doi.org/10.1007/b76881
ER  -